Fuzzy Parameters in the Analysis of Water Distribution Networks

Fuzzy analysis of water distribution networks (WDNs) determines how the uncertainties in independent or basic parameters (such as nodal demands and pipe roughness coefficients) are propagated to dependent or derived parameters (such as pipe flows, pipe velocities, and available pressure heads). Fuzzy analysis is useful in identifying the vulnerable zone in WDNs. Further, it can be used for the reliability analysis and reliability-based design of WDNs under uncertainty of various parameters. Several methodologies have been suggested for fuzzy analysis. These methodologies are categorized as: (i) optimization-based methodologies and (ii) analysis-based methodologies. The concepts behind these methods along with the brief description of various methods are provided. The membership functions obtained by both optimization- and analysis-based methodologies are compared with two example networks. At the end, methods for obtaining the approximate fuzzy membership functions are discussed.